$11^{1}_{3}$ - Minimal pinning sets
Pinning sets for 11^1_3 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_3 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 16
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.74309
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 6, 7, 8, 10}
7
[2, 2, 2, 2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
7
1
0
0
2.0
8
0
0
4
2.44
9
0
0
6
2.78
10
0
0
4
3.05
11
0
0
1
3.27
Total
1
0
15
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 4, 4, 7, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,7,7,2],[3,7,8,8],[3,8,8,7],[4,6,5,4],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[17,8,18,9],[10,2,11,1],[7,16,8,17],[2,12,3,11],[13,6,14,7],[15,4,16,5],[12,4,13,3],[5,14,6,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (1,10,-2,-11)(13,2,-14,-3)(11,4,-12,-5)(15,6,-16,-7)(9,18,-10,-1)(3,12,-4,-13)(5,14,-6,-15)(7,16,-8,-17)(17,8,-18,-9)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-11,-5,-15,-7,-17,-9)(-2,13,-4,11)(-3,-13)(-6,15)(-8,17)(-10,1)(-12,3,-14,5)(-16,7)(-18,9)(2,10,18,8,16,6,14)(4,12)
Loop annotated with half-edges
11^1_3 annotated with half-edges